Almost Everywhere Convergence of Inverse Dunkl Transform on the Real Line
| dc.creator | Kamel, Jamel El | |
| dc.creator | Yacoub, Chokri | |
| dc.date | 2007-06-25 | |
| dc.date.accessioned | 2026-07-07T08:12:13Z | |
| dc.date.available | 2026-07-07T08:12:13Z | |
| dc.description | In this paper, we will first show that the maximal operator $S_*^α$ of spherical partial sums $S_R^α$, associated to Dunkl transform on $\mathbb{R}$ is bounded on $L^p(\mathbb{R}, |x|^{2α+1} dx)$ functions when $\frac{4(α+1)}{2α+3}<p<\frac{4(α+1)}{2α+1}$, and it implies that, for every $L^p(\mathbb{R}, |x|^{2α+1} dx)$ function $f(x)$, $S_R^αf(x)$ converges to $f(x)$ almost everywhere as $R\to \infty$. On the other hand we obtain a sharp version by showing that $S_*^α$ is bounded from the Lorentz space $L^{p_i,1}(\mathbb{R}, |x|^{2α+1})$ into $L^{p_i,\infty}(\mathbb{R}, |x|^{2α+1}),\quad i=0,1$ where $p_0=\frac{4(α+1)}{2α+3}$ and $p_1=\frac{4(α+1)}{2α+1}$. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/0706.3619 | |
| dc.identifier | http://arxiv.org/abs/0706.3619 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132378 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Almost Everywhere Convergence of Inverse Dunkl Transform on the Real Line | |
| dc.type | text |